五十嵐治一
ニューロン系のエネルギー最小化による最適解探索に関する研究
Abstract:This paper deals with a neural computation approach that uses energy minimization to solve optimization problems. First, we propose a new method based on Hopfield's model, "Neural Relaxation Labeling Method", to solve problems of matching and recognizing patterns which consist of several straight line segments. Compatibility coefficients are usually calculated using a linear combination of several feature functions that represent disagreements between two pairs of primitives. Parameters, including proportional coefficients by which the feature functions are multiplied, can be determined by using a steepest descent method to decrease the value of the error function. Our simulations indicate that the present method, which uses the parameters mentioned above, has achieved more accurate matching and a higher level of recognition than those achieved by the classical relaxation labeling method by Rosenfeld, Hummel and Zucker.
Second, we propose a "Two-layer Random Field Model" (TRFM) to solve general combinatorial optimization problems and ill-posed problems within the framework of energy minimization. The new model consists of two layers of random fields. The lower layer is a random field that generates candidates for the optimal solution. Its probability distribution function is given by a Gibbs distribution function using an energy and a temperature. The upper layer is a field where constraints are represented. The two fields are loosely combined using a conditional probability. The values of parameters in the energy function, the regularization parameter or the weights of constraint terms, can be adjusted by our updating rule so that the energy minimum state satisfies the constraints represented on the upper layer. The energy minimum state can be found using the simulated annealing method, which enables TRFM to deal with non-linear or complicated energy functions.
In order to verify the parameter updating rule and the ability to find the optimal solution, we applied TRFM to three problems: image restoration using edge information, edge restoration from feature points and the traveling salesman problem. Experimental results show the effectiveness of TRFM for solving ill-posed problems and combinatorial optimization problems.